| Banach空间中两个极大单调算子公共零点的迭代格式 |
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| 引用本文： | 魏利,周海云.Banach空间中两个极大单调算子公共零点的迭代格式[J].数学研究及应用,2007,27(4):913-918. |
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| 作者姓名： | 魏利 周海云 |
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| 作者单位： | 1. 河北经贸大学数学与统计学学院,河北,石家庄,050061;军械工程学院应用数学与力学研究所,河北,石家庄,050003
2. 军械工程学院应用数学与力学研究所,河北,石家庄,050003;河北师范大学数学与信息科学学院,河北,石家庄,050016 |
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| 摘 要： | 令E为实光滑、一致凸Banach空间,E~*为其对偶空间.令A,B(?)E×E~*为极大单调算子且A~(-1)∩B~(-1)0≠(?).本文将引入新的迭代格式,利用Lyapunov泛函与广义投影算子等技巧,证明迭代序列弱收敛于极大单调算子A和B的公共零点.
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| 关 键 词： | Lyapunov泛函 极大单调算子 一致凸Banach空间. |
| 文章编号： | 1000-341X（2007）04-0913-06 |
| 收稿时间： | 2005/10/8 0:00:00 |
| 修稿时间： | 7/2/2006 12:00:00 AM |
An Iterative Algorithm of Common Zero Points for Two Maximal Monotone Operators in Banach Space |
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| WEI Li and ZHOU Hai-yun.An Iterative Algorithm of Common Zero Points for Two Maximal Monotone Operators in Banach Space[J].Journal of Mathematical Research with Applications,2007,27(4):913-918. |
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| Authors: | WEI Li and ZHOU Hai-yun |
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| Institution: | School of Mathematics and Statistics, Hebei University of Economics and Business, Hebei 050016, China; Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China;Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China; Institute of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China |
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| Abstract: | Let $E$ be a real smooth and uniformly convex Banach space with $E^*$ being its duality space. Let $A,B \subset E \times E^*$ be maximal monotone operators with $A^{-1}0\cap B^{-1}0 \neq \emptyset$. A new iterative algorithm is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators $A$ and $B$ by using the techniques of Lyapunov functional and generalized projection operator, etc. |
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| Keywords: | Lyapunov functional maximal monotone operator uniformly convex Banach space |
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